Hey Melissa,
Even if your doctor is right, and your suicidal thoughts will always be there, over time I think that you'll better be able to cope with them. You'll learn how to deal with your suicidal thoughts properly, and what to do when you may be having them. You'll also probably learn to keep them in the back of your mind, and as you continue with your recovery it will be easier to forget about them.
Don't take this as a bad thing, because everything can be worked through. Maybe your doctor told you this to make you more aware of your suicidal thoughts so that you can realize what provokes them and brings them to the front of your mind. This just might be one more step to recovering. Even if suicide is always looming in the back of your mind, you still have the possibility to be happy. You're not completely doomed, so don't lose hope.